It is shown how to extract the odds for getting different values of momentum from a generic wave function by writing it as a sum over functions of definite momentum. A recipe is given for finding states of definite energy, which requires solving a differential equation that depends on what potential the particle is experiencing. The particle in a box is considered and the allowed energies derived.

22 - Quantum Mechanics IV: Measurement Theory, states of definite energy

The fact that the wave function provides the complete description of a particle's location and momentum is emphasized. Measurement collapses the wave function into a spike located at the measured value. The quantization of momentum for a particle on a ring is deduced.

21 - Quantum Mechanics III

Lecture begins with a detailed review of the double slit experiment with electrons. The fate of an electron traversing the double slit is determined by a wave putting an end to Newtonian mechanics. The momentum and position of an electron cannot both be totally known simultaneously. The wave function is used to describe a probability density function for an electron. Heuristic arguments are given for the wave function describing a particle of definite momentum.

20 - Quantum Mechanics II

The double slit experiment, which implies the end of Newtonian Mechanics is described. The de Broglie relation between wavelength and momentum is deduced from experiment for photons and electrons. The photoelectric effect and Compton scattering, which provided experimental support for Einstein's photon theory of light are reviewed. The wave function is introduced along with the probability interpretation. The uncertainty principle is shown arise from the fact that the particle's location is determined by a wave and that waves diffract when passing a narrow opening.

19 - Quantum Mechanics I: Key Experiments and Wave-particle duality

Young's double slit experiment shows clearly that light is a wave. (In order to observe the wave behavior of light, the slit size and separation should be comparable or smaller than the wavelength of light.) Interference is described using real and complex numbers (in anticipation of quantum mechanics). Grating and crystal diffraction are analyzed.

18 - Wave Theory of Light

Ray diagrams are used to investigate the behavior of light incident on mirrors and lenses. The principle of least time is used to show that all rays from an object in front of a concave mirror focus on the image point if they are not too far from the axis. The experiments describing the breakdown of geometric optics are discussed.

17 - Ray or geometrical optics II

Geometric optics is discussed as an approximation to wave theory when the wavelength is very small compared to other lengths in the problem (such as the size of openings). Many results of geometric optics involving reflection, refraction (mirrors and lenses) are derived in a unified way using Fermat's Principle of Least Time.

16 - Ray or geometrical optics I

The physical meaning of the components of the wave equation and their applications are discussed. The power carried by the wave is derived. The fact that unlike Newton's laws, Maxwell's equations are already consistent with relativity is discussed. The existence of magnetism is deduced from a thought experiment using relativity.

15 - Maxwell's Equations and Electromagnetic Waves II

The various postulates of quantum mechanics treated in previous lectures are reviewed and summarized. The uncertainty principle is again discussed and a new one between energy and time is introduced. The quantum mechanical behavior of an electron in a hydrogen atom is described. The principles of quantum mechanics are then generalized to describe two or more quantum particles. It is shown that identical particles have to be bosons or fermions, the latter obeying the Pauli exclusion principle, which in turn is key to explaining the periodic table.

25 - Quantum Mechanics VII: Summary of postulates and special topics

The mathematics underlying LCR circuit theory for AC currents is discussed. Complex numbers are used to convert differential equations to algebraic equations. The notion of impedance is introduced. The radio is used to illustrate the concepts of resonance and variable capacitance. The body of classical electromagnetism treated so far is reviewed and summarized. The displacement current is introduced, leading to the complete Maxwell equations.

13 - LCR Circuits - AC Voltage

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Fundamentals of Physics, II - Video

Waves on a string are reviewed and the general solution to the wave equation is described. Maxwell's equations in their final form are written down and then considered in free space, away from charges and currents. It is shown how to verify that a given set of fields obeys Maxwell's equations by considering them on infinitesimal cubes and loops. A simple form of the solutions is assumed and the parameters therein fitted using MEs. The wave equation follows, along with the wave speed equal to that of light (3 x 108), suggesting (correctly) that light is an electromagnetic wave. The vector relationship between the electric field, the magnetic field and the direction of wave propagation is described.

14 - Maxwell's Equations and Electromagnetic Waves I

The allowed energy states of a free particle on a ring and a particle in a box are revisited. A scattering problem is studied to expose more quantum wonders: a particle can tunnel into the classically forbidden regions where kinetic energy is negative and a particle incident on a barrier with enough kinetic energy to go over it has a nonzero probability to bounce back.

23 - Quantum Mechanics V: Particle in a Box

The time-dependent Schrödinger Equation is introduced as a powerful analog of Newton's second law of motion that describes quantum dynamics. It is shown how given an initial wave function, one can predict the future behavior using Schrödinger's Equation. The special role of stationary states (states of definite energy) is discussed.

24 - Quantum Mechanics VI: Time-dependent Schrödinger Equation

Lecture begins with a discussion of electric potential distribution in conductors. Image charges are introduced and exploited. Capacitance is explained in greater detail and illustrated using the parallel plate capacitor. The energy stored in the electric field is derived. The forces acting on an electric current flowing through a conducting wire are examined. The RC circuits and its energetics are discussed. The EMF due to a battery is explained.

07 - Resistance

After a description of more complicated electric circuits, the basic ideas underlying magnetism are discussed and the relationship between electrical charges and magnetic fields is explored. Magnetism is caused and experienced only by moving charges. The Lorentz force on a charge is described and used to deduce the force on a current carrying wire. The cyclotron and velocity selector are described.

08 - Circuits and Magnetism I

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